Friday, November 18, 2016

Anyone who makes an effort to study monetary economics quickly encounters the concept of Gresham's law, or the idea that bad money can often chase out good. Gresham's law is usually used to explain the failures of bygone monetary systems like bimetallic and coin standards. But the phenomenon isn't confined to ancient times. I'd argue that a modern incarnation of Gresham's law is occurring right now in Zimbabwe.

Zimbabwe's stock market has blown away all other stock markets by rising 30% in the last month-and-a-half. The chart below compares the Zimbabwe Industrial index to the U.S. S&P 500, both of which are denominated in U.S. dollars. I'd argue that the extraordinary performance of Zimbabwean stock is an instance of Gresham's law. With the imminent arrival of newly printed Zimbabwean paper money, known as bond notes, "bad" paper money is poised to chase out "good" money, stocks being one of the few places where Zimbabweans can protect their savings.

What follows is a quick summary of bond notes (alternatively, read my twoearlier posts). The Mugabe government, which began discussing the idea of a new paper currency earlier this year, says that it will issue low denomination bond notes into circulation before the end of the November. Recall that Zimbabwe has been using U.S. dollars since 2008 after a brutal hyperinflation destroyed the value of the local currency. The regime claims that a $1 bond note will be worth the same as a regular $1 Federal Reserve note. It says it has received a U.S. dollar line of credit from the African Export-Import Bank that will guarantee the peg.

Enter Gresham's law, which says that if two different media circulate, and the government dictates that citizens are to accept the two instruments at a fixed ratio—say via legal tender laws—then the undervalued medium will disappear leaving only the overvalued one to circulate. So called bad money drives out good.

Medieval coinage systems were often crippled by Gresham's law. For instance, say a new debased silver penny was introduced into circulation along with existing pennies. Because it contained a smaller amount of silver, the new penny was worth less than the old. However, legal tender laws required that all pennies be accepted without discrimination in the settlement of debts. Medieval debtors would thus always prefer to discharge debts with new pennies rather than old ones since they would be giving up less silver. The result was that only "bad money," or debased coinage, circulated. Because "good money," or undebased coinage, was undervalued, people either hoarded it, sent it overseas, exchanged it on the black market at its true value, or melted it down.

The same conditions that created Gresham effects in medieval times are emerging in modern day Zimbabwe. Rather than two different medieval coins, we've got two different types of dollars; bond notes and regular U.S. cash. The next ingredient for Gresham's law is a decree that dictates the rate at which people are to accept the two instruments. In Zimbabwe's case, the government has already declared that bond notes (once they appear) are to be legal tender along with U.S. Federal Reserve notes, which means that Zimbabwean creditors will have to accept bond notes at par as a means of discharging all debts, even if they'd prefer the genuine thing.

Since a chequing deposit is a debt incurred by a bank to a depositor, this means that Zimbabwean banks can—in theory at least—meet depositors' demands for redemption by providing bond notes. So a Zimbabwean bank deposit is no longer just a claim on actual dollars, but a claim on some mysterious as-yet unissued Zimbabwean government liability.

The last ingredient for Gresham's law is an overvaluation of one of the two media. In Zimbabwe, this will most likely occur as the market value of bond notes falls below that of genuine U.S. dollars. While many countries maintain successful currency pegs to the U.S. dollar, they have the resources to do so. I'm skeptical that the isolated and corrupt Mugabe regime has the resources to pull a peg off.

Bond notes have yet to be issued, but because existing bank deposits—or electronic dollars—are likely to be payable in this new paper currency, we can think of deposits as a surrogate for the bond note. The first bit of evidence that Zimbabwe has run into Gresham's law is that physical U.S. dollars are beginning to disappear from circulation, replaced entirely by electronic dollars. Why might this be happening? Start with the assumption that Zimbabwean bank deposits have become "bad," meaning they are worth less than actual physical dollars. If a Zimbabwean citizen needs to buy $100 in groceries, and the grocer is required by law to accept deposits and cash at the same rate, our citizen will naturally spend only overvalued deposits and hoard "good" and undervalued cash.

In fact, we have direct evidence that deposits have become "bad". In the black market, dealers will only sell physical cash at apremium. I've seen anywhere from 5% to 20% mentioned.

More evidence is provided from the stock market. The shares of Old Mutual, a global financial company, trade on both the Zimbabwe Stock Exchange (ZSE) and the London Stock Exchange (LSE). Because investors have the ability to deregister their shares from one exchange and transfer them for re-registration on the other, arbitrage should keep the prices of each listing in line. After all, if the price in London is too high, then investors need only buy the shares in Zimbabwe, transfer them to London, sell, and repurchase in Zimbabwe, earning risk-free profits. If the price in Zimbabwe is too high, just do the reverse

Oddly, Old Mutual trades in London for around $2.30 per share (after converting into US dollars) whereas it is valued at $3.20 in Zimbabwe. Here's the article that first tipped me off to this. As the chart below shows, this rather large gap has progressively emerged as the introduction of bond notes becomes more likely. Why is no one arbitraging the difference by purchasing Old Mutual in London for $2.30, then transferring it to Zimbabwe to be sold for $3.20? The large discrepancy likely reflects the growing risk that any dollar sent to Zimbabwe is likely to be trapped and re-denominated into a bond note.

The ratio of the two Old Mutual listings implies that the exchange rate between genuine U.S. dollars and dollars held in Zimbabwe is around 0.72:1, i.e. one Zimbabwean U.S. dollar deposit is only worth 72 cents in genuine U.S. dollars. While transaction costs and other frictions may explain part of the gap, this is still an incredibly wide discount.

Those with long memories will remember that during Zimbabwe's last hyperinflation, the cross-rate between Old Mutual listings was a popular way to measure the true exchange rate between the hyperinflating Zimbabwe dollar and the U.S. dollar. The official rate maintained by the Reserve Bank of Zimbabwe was not the true rate as it dramatically overvalued the Zimbabwe dollar. In the chart below of the hyperinflation, pinched from a paper by Steve Hanke, the Old Mutual Implied Rate—or OMIR—appears along with the black market rate for U.S. dollars. (I once discussed the OMIR here. The same trick was used in Venezuela using ADRs.)

Once all the ingredients for Gresham's law are in place, inflation is never far behind. Because U.S. dollars are being undervalued, Zimbabweans will refuse to buy stuff with anything other than overvalued deposits. If they don't update their sticker prices, retailers will soon discover that they are receiving fewer real dollars than before. To maintain the real value of their revenues, they will have to mark up their prices, thus compensating for the fact that only "bad" money is flowing into their tills.

While retail prices are usually sticky, financial prices are not. And that may be why we've seen such a huge jump in Zimbabwean stock prices but little movement in Zimbabwean consumer price inflation. With Gresham's law beginning to push good money out of circulation, nimble owners of Zimbabwean shares are demanding a higher share price from potential share buyers in order to compensate for the risk of holding soon-to-be issued bond notes. Less nimble retailers have yet to demand this same compensation from their customers. Don't expect this to last; consumer price inflation can't be too far behind asset price inflation.

Sunday, November 13, 2016

Prime Minister Narendra Modi's aggressive demonetization of the 500 and 1000 rupee note is causing plenty of chaos in India. A general shortage of money has emerged, massive lineups have formed at banks, and cash-based business has come to a standstill. All this would seem to indicate that the process has been ineptly carried out. But I'd argue that the problems listed above are exactly what one should expect of a well-designed aggressive demonetization. Chaos is a feature, not a bug.

As I mentioned in my previous post, a regular demonetization isn't meant to harm anyone. To ensure that no one is left behind, legacy note are gradually replaced with new ones, a process that often takes decades to carry out. See for instance the below pamphlet published by the Bangko Sentral ng Pilipinas (BSP), the Philippines central bank. It shows a slow and staged approach to replacing old peso notes with new ones. The goal of an aggressive demonetization like Modi's is exactly opposite: to leave people behind. To get this effect, the demonetization has to begin suddenly and end quickly.

Why didn't Modi make more preparations for the retirement of the Rs 500 and 1000 note? For instance, to reduce lineups at banks and ATMs the Reserve Bank of India could have begun supplying banks with extra 100 rupee notes several weeks ago in order to ensure that there was sufficient supply come November 8. And maybe the RBI could have nudged banks to purchase more safety deposit boxes to hold cash and hire extra staff to handle the rush.

Or take ATMs. One reason for lineups is that with the demise of the 500 and 1000 note, ATMs are running at a fraction of their capacity. Indian ATMshave four "cassettes", each holding around 2000 notes. Two cassettes are typically configured for the old 500 rupee note, one for the legacy 1000, and one for the still-existing 100. They typically do not dispense 50s. Thus the maximum an Indian ATM can provide in a post-demonetized India is one cassette worth of 100s, or 200,000 rupees (US$3,000). If everyone in the lineup removes 2000 rupees, the daily limit, that means just 100 people can be served. That's peanuts.

To get ATMs up to full capacity, all four cassettes need to be dispensing some combination of new 500 notes, 2000 notes, and/or existing 50 and 100 notes. The problem is that each ATM cassette need to be re-calibrated to hold a certain denomination since notes are not uniformly shaped. With every single ATM in the country needing to be modified, and only so much staff trained to do so, it's taking a lot of time.

So why didn't the government begin working with ATM companies a few months ago to make all the modifications in time for November 8? This would have surely reduced the awful indignities that regular Indians must undergo as they wait for hours to withdraw cash.

Unfortunately, any attempt to modify ATMs ahead of time would have caused Modi's aggressive demonetization to fail. In order to inflict maximum damage on those who depend on "black money" (i.e. income obtained illegally or not declared for tax purposes), an aggressive demonetization needs to be executed suddenly. If rumour gets out that a demonetization is about to occur, the element of surprise will be lost. Those working in the underground economy will simply switch their high value banknotes into low ones ahead of the demonetization, thereby avoiding being damaged. And of course it is the rich, not the poor, who have the best networks for gleaning information. To reduce the potential for information leaks, the number of people 'in the know' needs to be kept to a minimum, and this means that all large-scale preparation—including a huge reconfiguration of the ATM network—must be avoided.

So if you support the idea of a demonetization—specifically one that is designed to hurt the underground economy and, in so doing, draw people into the taxed economy--then you should just accept that this was always going to be a messy affair. If it had been a smooth one, then that would have been a sign that it wasn't being effective.

Once the dust is settled, India will be made better off by the demonetization. While many Indians in the underground sector will grudgingly comply and deposit their funds in an account only to withdraw that same amount in new notes later, others will keep their funds in the banking system. To change, people sometimes need to be prodded. This should be a shift in the right direction given that a banked economy is stronger than an unbanked one.

My back of the envelope calculation tells me that the demonetization will generate real pain on the underground economy. Consider that there are Rs 12.2 trillion worth of 1000 and 500 notes in circulation, or US$181 billion (source). Assume that 40% of these notes, or Rs 4.9 trillion (US$72.7 billion) circulate in the dark economy and lack a paper trail. Further assume that thanks to Indian ingenuity, or jugaad, half of the black money will sneak through the demonetization. That still leaves the remaining Rs 2.4 trillion, or US$36 billion, stranded. That's a painful writeoff!

To build and effectively run a nation, a government needs to be able to efficiently collect taxes. Many will shrug off the immense losses caused by the demonetization and go back to using cash as a way to evade to avoid the tax man, especially now that the government has (somewhat puzzlingly) introduced a new 2000 rupee banknote. But a large enough contingent will migrate to the tax-paying economy for good. Once bitten, twice shy.

Tuesday, November 8, 2016

Prime Minister Narendra Modi surprised Indians today by announcing that India's highest denomination notes, the 500 and 1000 rupee, will cease to be legal tender. On first blush, India seems to be enacting Ken Rogoff's idea of cutting down on criminality and tax evasion by phasing out high-denomination notes, which I recently discussed here.

But this isn't the case. Rather than removing the Rs. 500, the Reserve Bank of India is replacing it with a new bill. Furthermore, it will also be issuing a Rs. 2000 note, a new highest denomination note. What India is doing is enacting what I'll call an aggressive demonetization. I'd argue that this is an alternative (though not mutually exclusive) idea to Rogoff's. Both schemes are intended to create a logistical nightmare for money launderers; but whereas Rogoff's entails altering the denomination structure of banknotes to get this effect, Modi's aggressive demonetization keeps that structure intact while using note redemption and re-issuance as its lever.

Demonetizations are usually non-aggressive drawn-out affairs. For instance, when Canada announced that it would withdraw its $1000 note, it gave Canadians an eternal window to bring them in for redemption. The $1000 remains legal tender in Canada, meaning that it can be used to discharge any debt. As another example, take the euro. The introduction of the euro meant an end to all the national European currencies. While each of these currencies lost legal tender status in 2002, many enjoy an unlimited time frame for conversion into euros, including the Deutsche mark and Belgian franc. See below:

India's demonetization is an aggressive one because legal tender status is to be removed immediately and the time limit for redemption is incredibly tight and scripted. Here is Modi's announcement:

To summarize, Indians have just a few weeks to exchange old notes for new ones at banks or post offices. Proof of ID is required and switches are limited to Rs 4000, around US$60. There is no size limit for directly depositing old notes in bank of post office accounts. But of course, this means that the depositor's identity will be known by the bank and transactions will be traceable. Deposits can be made at banks until the end of the year. After that date, the central bank will exchange old notes until March 31, 2017, although this will require some sort of declaration of origin.

The point of all this is to suss out anyone with large amounts of cash that has been earned from dubious sources. Say you've got one million paper rupees, worth around US$15,000. If you've got the receipts to show why you have that much cash, then you can safely bring it to the bank. But if you don't, you'll have to get rid of it as quick as you can by spending it, say on gold (or any other good). However, this will be an incredibly difficult task given the fact that there will be many other Indians trying to spend their undocumented Rs. 1000 and Rs. 500 notes on gold at that very same time, and only a limited number of gold dealers willing to accept them. After all, any gold dealer who accepts notes now inherits the same problem: what to do with newly-demonetized banknotes. Any gold dealer who starts to bring in larger-than-normal amounts of paper money to their bank for redemption will surely face questions. To compensate for this risk, gold dealers will either impose a large penalty on cash payments or they'll stop accepting cash altogether.

Some undocumented rupees will no doubt be successful in evading Modi's aggressive demonetization, but large quantities will be left stranded. Significant damage will have been dealt to anyone working in the underground economy.

As Tony Yates points out, the most aggressive demonetization in history was probably Saddam Hussein's recall of the Swiss dinar in 1993. Swiss dinars were Iraqi banknotes printed on high quality paper whereas dinars printed after the 1992 U.S. invasion were issued on shoddy and easily counterfeitable material. On May 5, Saddam announced that all Swiss dinars had to be turned into the central bank for an equivalent amount of post-war currency over a tiny six day exchange period. He then proceeded to close the border, preventing Kurds and other foreigners from making the switch. Huge amounts of currency was left stranded, although unlike the Indian situation it was foreigners, not criminals/tax evaders, who were the target. (I went into the Iraq story here. The Burmese kyat and North Korean won demonetizations of 1985 and 1999 were also quite awful, see here.)

If you think Modi's strategy is new, or confined to developing nations, think again. A few years ago, Sweden carried out out a (somewhat less) aggressive demonetization in order to catch illicit cash users. In 2012, the Riksbank announced that all 1000 krona banknotes without foil strips were to be declared invalid by the end of 2013 (each 1000 krona note is worth around $110). Until December 31, 2013, Swedes were permitted to get rid of 1000 krona notes by either using them to buy stuff or depositing them at a bank. To tighten the noose, no anonymous conversions of old notes into existing notes were permitted. Swedes had to have bank accounts, and therefore had to forgo their anonymity, in order to rid themselves of old currency.

Anyone who's seen Breaking Bad knows that laundering money takes time and patience. A Swedish criminal with ten million dollars worth of high denomination krona was suddenly faced with a significant problem; how to get this stash back into the legitimate economy within 400 or so days.

How tough was this challenge? We know that at the start of 2013 there were fourteen million 1,000 krona notes in circulation (worth 14 billion SEK, or US$1.6 billion). After the expiry date, the Riksbank noted that there were still some three million 1,000 krona notes that had not been redeemed, worth around $330 million. This gives a rough indication of the value of banknotes left stranded by criminals and tax evaders, around 25% of all notes outstanding.

After the December 31, 2013 deadline, the Riksbank itself offered to redeem invalid banknotes (it still does), albeit for a 100 krona fee. However, criminal and tax evaders have no doubt steered clear of this offer as the declaration form includes the following question:

Sweden is the only country in the world in which cash holdings are in decline. Might this have had something to do with the damage inflicted by the Riksbank's 2013 demonetization on the psyche of participants in the underground economy?

So let's compare the advantages of Modi's aggressive demonetization to Rogoff's abolition of high denomination notes. If an aggressive demonetization is chosen, then a central bank gets to enjoy high profits, or seigniorage, since it continues to issue an extended range of banknotes, unlike Rogoff's abolition. The more float, or 0% cash liabilities that remain outstanding, the more interest the central bank will earn on its bond portfolio. The central bank also earns significant earnings from 'breakage.' All illegitimate banknotes that never get redeemed are recognized as a one-time unusual gain on the central bank's statement of income. Finally, people engaging in legal activities who enjoy the anonymity afforded by high denomination notes still get to use them; they don't under Rogoff's abolition.

Unfortunately, an aggressive demonetization can only be effective for a little while. It's hard to see why people won't quickly re-adopt the highest denomination note as a medium for evading taxes and engaging in illicit activity. In response, the central bank will have to enact an followup demonetizations every few years, but of course the underground economy will do its best to anticipate these by moving into low-denomination notes or foreign paper whenever it suspects something is afoot.

"Why not simply increase the physical dimensions of high-denomination notes without jumping through the flaming hoop of elimination? Before 1929, U.S. currency was 40 percent physically larger than it is now. Restoring that size or making it even larger would instantly work the wonders of decades of inflation. The iron law for subverting illicit economies: a percentage increase in physical note size is equivalent to the same percentage increase in the price level."

Sunday, November 6, 2016

The US$5000 banknote, destroyed in 1969 along with the $10,000, $1000, and $500 notes

With the publication of his new book The Curse of Cash, economist Ken Rogoff has ignited a big debate over the future of paper money. Both the book, which is packed with information and accessible to a mainstream audience, and Rogoff's series of blog posts are well worth reading, even if you already disagree with his premise that the way the world currently handles cash needs to be modified.

The key observation motivating Rogoff's book is this one: with $1.3 trillion worth of U.S. currency in existence, a back-of-the-envelope calculation says that the average four person family should be holding around $16,800 in cash. However, this simply doesn't reflect the personal experience of most Americans. Indeed, 2012 survey data shows that consumers generally report holding just $56 per person, leaving the majority of cash unaccounted for. Nor is this anomaly confined to the U.S. Given $78 billion in Canadian currency outstanding, a four person family in Canada should hold around $6,000. Instead, survey data shows the average person only holds a median $38 in their wallets. The same pattern occurs in Europe, Japan, Australia, and elsewhere.

According to Rogoff, much of the unaccounted cash is being held by those who participate in the underground economy, both by those engaged in criminal activity and those employed in legal activity (dentists, contractors, retailers, etc) who use cash as a way to avoid taxes. Rogoff's premise is that if we can alter the institution of cash, then maybe we can flush some of these people out of the underground economy and back into the legal, tax-paying economy.

The denomination structure of cash

Having read through many of the criticisms that Rogoff has received over the last few months, I've noticed that there is a tendency on the part of his opponents to frame this debate as an either/or one. Either keep cash and the personal liberty it provides—anonymity and uncensored access to the payments system—or sacrifice cash and in the process throw out that liberty.

This mischaracterizes the debate. Rogoff isn't advocating an end to cash or the liberties that go with it. Rather, he wants a modification of the existing denomination structure of banknotes such that the $100, $50, and $20 are removed while the $1, $2, $5 and $10 are left in circulation. Over the long-term, he proposes replacing these small bills with heavy coins. The set of personal liberties afforded by cash will be allowed to live on, albeit through the reduced convenience of small banknotes like the $10.

The term denomination structure refers to the top and bottom-most denominations issued by the monetary authority, the spacing between denominations, and the point at which the transition between coins to notes begins. As per Tyler Cowen's second law ("There is a literature on everything"), academics have been writing on the topic of optimal denomination structure for a few decades. The goal of this literature is to find the range and spacing of notes/coins that reduces the amount of monetary work that all participants in a currency system must engage in. By monetary work, I mean the effort that goes into printing money, carrying it, storing it, counting it, making calculations with it, paying with it, and breaking it into smaller amounts. If a denomination structure can be found that allows everyone do a little bit less work, society is much better off.

Rogoff takes the opposite approach. His abolition of large denomination banknotes is designed to increase rather than reduce the amount of monetary work that users of cash must engage in. After all, ten thousand dollars worth of Rogoff's preferred highest value note—the $10 bill—requires far more effort to count, store, and lug around than a hundred $100 bills.

Rogoff believes that the increase in monetary work brought about by a reduction in the purchasing power of the highest value note can be a useful filtering mechanism for improving societal welfare. Assume that there are "bad" and "good" users of cash, the former being criminals and tax evaders and the latter being regular people who want to enjoy the speed, anonymity, and convenience of paper money. "Good" cash users only need small quantities of notes from time to time and therefore will only be slightly inconvenienced by the increase in monetary work caused by a constriction in the purchasing power of the highest denomination note. "Bad" users tend to make regular use of large amounts of cash, and will therefore be severely affected by a constriction.

While Rogoff's abolition won't stop crime or tax evasion, it will surely make these activities trickier. This should in turn push activity out of the non-taxed underground economy into the legal economy.

Burdening cash is the status quo policy

These ideas aren't entirely novel. In fact, I'd argue that since the 1800s, the U.S. has been implicitly adopting Rogoff's strategy of increasing the amount of monetary work involved in using cash. The chart below illustrates both the nominal and real value (in 2015 dollars) of the U.S.'s highest denomination banknote going back to 1871.

In general, the purchasing power of the highest denomination note has been gradually declining. This has been mostly due to the fact that even as inflation erodes the dollar's value, American monetary authorities have chosen to avoid introducing new higher value notes. Nor is the U.S. unique in this respect. Correct me if I'm wrong, but I can't think of a single developed nation that has introduced a higher denomination note over the last fifty years.

In the U.S.'s case, the decline in the purchasing power of the highest denomination note hasn't been entirely due to the combination of inflation and a lack of new large value U.S. notes. Take a look at what happened in 1969. Throughout the 19th century the U.S. Treasury was an issuer of $10,000 certificates, a practice the Federal Reserve would continue after its founding in 1913. However, on July 14, 1969 the Fed announced that it would put an end to this tradition by destroying all $10,000, $5000, $1000, and $500 denominations, leaving the $100 as the U.S.'s largest denomination. It did so on the very same day that Richard Nixon launched his famous war on drugs. Although the Fed claimed that its decision was motivated by the declining usage of large value banknotes over the previous two decades (PDF pg 624), the timing indicates that Nixon's crime push must have been a big reason.

So largely through a policy of benign neglect (i.e. by passively allowing inflation to eat away at its purchasing power), the U.S. along with most developed nations have been gradually increasing the workload involved in using the highest value note. Assuming inflation of 2%, by 2095 or so the US$100 will buy as much as the $20 does today. By 2130, it will buy as much as the $10 does today.

Rogoff isn't content with the gradual approach to increasing monetary work. He wants to add a one-time increase in the level of monetary work involved in using cash. This would involve a quick Nixon-style "tightening" of the filter, removing in one fell swoop all denominations above the $10 bill. Put differently, rather than waiting till 2130 for the $100 bill to be worth $10, he wants this event to happen now. Once a Rogoff-style high denomination notes abolition has been carried out, inflation will once again determine the rate of increase in the monetary work involved in cash usage.

So ultimately, the great cash debate isn't about cash vs. cashlessness. For decades developed nations have been gradually increasing the burden of using banknotes. Should we stick with the status quo or speed things up a little?

The case of Sweden

Rogoff makes one mistake in his book. As many people may know, Sweden is the only nation in which cash usage is in decline, a precedent Rogoff wants other nations to emulate. Several times in his book, Rogoff mentions that the Swedes have removed their highest denomination note, the 1,000 kronor, and that this removal helps to explain the nation's dramatic drop in cash usage. But this isn't the case. All that the Riksbank did was replace the old 1,000 kroner note in 2013 (which had Gustav Vasa on it) with a new Dag Hammarskjöld version. The 1,000 is still alive and kicking.

This puts Rogoff in a somewhat uncomfortable position. Some other policy than the one he prefers is at work in the very country he puts forth as an example for all to follow. I think I might know what this policy is. As discussed in this excellent post by Martin Enlund, the Swedes implemented a tax deduction in 2007 for the purchase of household-related services such as the hiring of gardeners, nannies, cooks, and cleaners. This initial deduction, called RUT-avdrag, was extended in 2008 to include labour costs for repairing and expanding homes and apartments, this second deduction called ROT-avdrag.

Enlund's chart shows how the decline in krona outstanding closely coincides with the timing of the introduction of RUT and ROT:

Prior to the enactment of the RUT and ROT deductions, a large share of Swedish home-related purchases would have been conducted in cash in order to avoid taxes, but with households anxious to claim their tax credits, many of these transactions would have been pulled into the open. Note the rise in RUT and ROT payments on Enlund's chart, for instance. Calleman reports that the number of customers using registered domestic service companies rose from 92,000 in 2008 to 537,600 in 2013. Since the implementation of RUT and ROT, Swedish opinions on paying for undeclared work have changed dramatically. In 2006, 17% said it was completely wrong to to hire undeclared labour. In 2012, 47% felt it was completely wrong.

Using data from a survey of the general public conducted by the Swedish tax authority, the charts below show how much knowledge Swedes have about those around them engaged in tax evasion. In the bottom chart, the number of Swedes who are aware of businesses that are evading taxes has fallen from 27% in 2007 to just 9% in 2013. That is an especially large and fast decline. As the tax authority points out, RUT and ROT is the likely explanation.

Rogoff himself maintains in The Curse of Cash that the largest holdings of cash in the underground economy are due not to criminals but those engaged in legal work (like contractors) who are avoiding taxes. By cutting down dramatically on tax evasion among those engaged in household services and repairs, the RUT and ROT deductions may explain a significant chunk of the decline in Swedish currency in circulation.

This post has gone long enough, so let me get to my final point. I agree with Rogoff's general point that it makes sense to burden cash users with ever more work since this burden disproportionately falls on heavy users like criminals. But Rogoff hasn't yet convinced me that the status quo policy of gradually increasing the workload involved in cash usage (via inflation) needs to be sped up by a sudden removal of every bill above the $10. After all, the Swedes are setting an example of how a policy of gradualism can be twinned with tax policy in order to get some of the very effects that Rogoff advocates, namely pulling people out of the underground economy into the legal economy.

Is the Swede's approach better than Rogoff's high denomination note abolition? I'm not sure, I don't know enough about the economics of tax policy to arrive at a firm conclusion. But it seems to me that a more complete analysis of the real reasons for Sweden's cash miracle needs to be conducted before we go about killing the $20, $50, and $100.